Render a layer only once for all 1800 frames?
Okay, so I rendered all the layers together for the first frame, but with compositing checked off. Then, in the image result viewer I selected only the atmosphere render result, saved that layer as a PNG, and then imported that PNG into the compositor as an image input node, replacing the atmo render layer input node and its connections.

Then to render the animation, I will uncheck or entirely delete the atmosphere object and render layer from the project, and Blender will now render the planet for each frame and composite that render layer with the single atmosphere image.

I did a quick test of render time for 27 frames (just an arbitrary number of frames I decided to stop on), and for this method, the render time was about 62% that of the old method.

Many thanks to @cegaton for the help, I feel weird answering my own question though.